The Sharks are also without center Logan Couture, who will miss his fifth straight game since being hit in the mouth by the puck after a deflection of a shot by defenseman Brent Burns against the Nashville Predators on March 25.
"I expect both of them will be back at some point," DeBoer said. "Until then, I'm going to call it day to day. I don't have a time frame on it."
Couture hasn't skated since he was injured but hopes to return for the Stanley Cup Playoffs, which begin next week. The Sharks (44-28-7) have clinched a berth and are two points behind the Edmonton Oilers for second place in the Pacific Division. San Jose is 2-8-0 in its past 10 games.
"I'm going to try to," said Couture, whose 52 points (25 goals, 27 assists) in 73 games are third on the Sharks, when asked about returning. "That's the goal, to play hockey. Today was a good day for me. Get some exercise and feel good and we'll go on to tomorrow. When we get there I'll see what I can do."
Couture said he's been able to eat solid foods, thanks to the medical care he received in Nashville, and hasn't lost weight.
"Right when it happened I went to the Nashville room," Couture said. "Their doctors and dentists did a great job trying to basically save my teeth. They had to move a lot of them around. Obviously from the impact of the puck, they were all shifted in my mouth. [They] did a great job at that time to try and save them.
"I went to Vanderbilt Hospital. They brought a guy in there to put what they call an arch bar on my teeth to try and save them. ... They're all damaged. A lot of these teeth are going to be taken out at some point once the season's over."
With Thornton and Couture out indefinitely, the Sharks will have to find a way to survive without two players who were critical to their run to the 2016 Stanley Cup Final.
"Obviously it's a little different look for us, but we've had depth on this team," captain Joe Pavelski said. "And I think the structure to our system and our team game, it doesn't just rely on one guy or two guys. You don't get to where we were last year on one guy or two guys. ... If we can all kind of rally together, there's no reason we can't get the job done and be successful moving forward."